Mistress Quickly of The Merry Wives of Windsor is not the same Mistress Quick-LAY of the Henriad. While she is still unintentionally bawdy ("up early and down late" [I.iv.94]), the context is completely different. In the Henriad, the tavern is often mistaken as a bawdy house (or IS that a mistake), so her bawdiness there makes sense. Here, as the "dry nurse" (I.ii.3) to Doctor Caius, it feels out of place.

Or is it just that here it is more intentional?

Could she be the Elizabethan forerunner of Mrs. Roper???